Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 + 8 x + 88 x^{2} + 381 x^{3} + 2024 x^{4} + 4232 x^{5} + 12167 x^{6}$ |
| Frobenius angles: | $\pm0.539863130869$, $\pm0.585825226110$, $\pm0.646007100358$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.1374646931.1 |
| Galois group: | $A_4\times C_2$ |
| Cyclic group of points: | yes |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $3$ |
| Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $18901$ | $182564759$ | $1734721248637$ | $21824664132972779$ | $267121498842929193511$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $32$ | $642$ | $11711$ | $278690$ | $6448072$ | $148030017$ | $3404632928$ | $78311476866$ | $1801154606276$ | $41426502016322$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains no Jacobian of a hyperelliptic curve, but it is unknown whether it contains a Jacobian of a non-hyperelliptic curve.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{23}$.
Endomorphism algebra over $\F_{23}$| The endomorphism algebra of this simple isogeny class is 6.0.1374646931.1. |
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
| Twist | Extension degree | Common base change |
|---|---|---|
| 3.23.ai_dk_aor | $2$ | (not in LMFDB) |